Media Storage Type : 32 GB USB Stick
NPTEL Subject Matter Expert : Prof. Suprio Bhar
NPTEL Co-ordinating Institute : IIT Kanpur
NPTEL Lecture Count : 40
NPTEL Course Size : 2.4 GB
NPTEL PDF Text Transcription : Available and Included
NPTEL Subtitle Transcription : Available and Included (SRT)
Lecture Titles:
Lecture 1 - Introduction to the course Measure Theoretic Probability 1
Lecture 2 - Sigma-fields and Measurable spaces
Lecture 3 - Fields and Generating sets for Sigma-fields
Lecture 4 - Borel Sigma-field on R and other sets
Lecture 5 - Limits of sequences of sets and Monotone classes
Lecture 6 - Measures and Measure spaces
Lecture 7 - Probability Measures
Lecture 8 - Properties of Measures - I
Lecture 9 - Properties of Measures - II
Lecture 10 - Properties of Measures - III
Lecture 11 - Measurable functions
Lecture 12 - Borel Measurable functions
Lecture 13 - Algebraic properties of Measurable functions
Lecture 14 - Limiting behaviour of measurable functions
Lecture 15 - Random Variables and Random Vectors
Lecture 16 - Law or Distribution of an RV
Lecture 17 - Distribution Function of an RV
Lecture 18 - Decomposition of Distribution functions
Lecture 19 - Construction of RVs with a specified law
Lecture 20 - Caratheodery Extension Theorem
Lecture 21 - From Distribution Functions to Probability Measures - I
Lecture 22 - From Distribution Functions to Probability Measures - II
Lecture 23 - Lebesgue-Stieltjes Measures
Lecture 24 - Properties of Lebesgue Measure on R
Lecture 25 - Distribution Functions and Probability Measures in higher dimensions
Lecture 26 - Integration of measurable functions
Lecture 27 - Properties of Measure Theoretic Integration - I
Lecture 28 - Properties of Measure Theoretic Integration - II
Lecture 29 - Monotone Convergence Theorem
Lecture 30 - Computation of Expectation for Discrete RVs
Lecture 31 - MCT and the Linearity of Measure Theoretic Integration
Lecture 32 - Sets of measure zero and Measure Theoretic Integration
Lecture 33 - Fatou's Lemma and Dominated Convergence Theorem
Lecture 34 - Riemann and Lebesgue integration
Lecture 35 - Computations involving Lebesgue Integration
Lecture 36 - Decomposition of Measures
Lecture 37 - Absolutely Continuous RVs
Lecture 38 - Expectation of Absolutely Continuous RVs
Lecture 39 - Inequalities involving moments of RVs
Lecture 40 - Conclusion to the course Measure Theoretic Probability 1